Genetic crosses in model organisms play an essential role in understanding how heritable factors affect medically relevant traits. Such crosses have traditionally tended to be on a small scale with limited power to detect genetic effects, limited ability to localize causal variants, and limited options for replication. In the last decade, however, the emergence of larger-scale interdisciplinary research, cheaper genotyping and parallel advances in human genetics, has spurred the development of more sophisticated and powerful experimental designs. Foremost are those that incorporate two modern genetic design concepts: the multiparental population (MPP), whereby each subject is descended from a small, well-characterized set of genetically diverse inbred strains, with the goal of efficiently exploring a wide genetic landscape; and the genetic reference population (GRP), whereby subjects are drawn from a large and genetically diverse set of inbred strains, with the goal that the study population, and thereby the studies themselves, can be infinitely replicated. Their combination, the multiparental genetic reference population (MP-GRP), represents the state-of-the-art in complex trait genetics and has been implemented in a number of model organisms, including plants, flies, and rodents. The proposed program of research focuses on the development of statistical and computational tools to advance the design and analysis of studies using MPPs, GRPs and MP-GRPs. It centers around addressing three interconnected questions. 1) How to take advantage of biological replicates in a genetically varying population? Directions considered include: more stable methods to detect genetically-induced phenotypic outliers; use of genetically-induced heteroskedasticity to improve statistical power and find variance-controlling genes; and more rigorous and expansive characterization of gene-by-treatment effects by using principles from causal inference. 2) How to navigate the complex design space of MP-GRPs and their derived crosses? Directions considered include: use of decision theory applied to Bayesian analysis of pilot data; incorporation of variance heterogeneity to control likely reproducibility. 3) How to approach quantitative trait locus (QTL) analysis in MPPs and MP-GRPs? Directions considered include: making haplotype-based association more robust to uncertainty in haplotype state; combining haplotype- based with variant-based mapping; adaptive modeling of QTL complexity; machine learning of the allelic series; familywise error rate control through descent-based permutation. Progress on these fronts will not only fill significant gaps in studies using MPPs, GRPs and MP-GRPs, but will also provide tools and insights that will allow these designs to be used in new and more powerful ways.